Abstract:Singular quadratic functionals of one dependent variable with nonseparated boundary conditions are investigated. Necessary and sufficient conditions for nonnegativity of these functionals are derived using the concept of {coupled point} and {singularity condition}. The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.
Keywords: quadratic functional, singular quadratic functional, periodic and antiperiodic boundary condition, conjugate point, coupled point, singularity condition
AMS Subject Classification: 34C10, 49B10, 34A10